Simulated Bernoulli and Binomial Proportion Data

bernoulli_data() creates a simulated univariate Bernoulli data set having a dependent variable dv with values of 0 and 1, and an independent variable iv with levels represented by lower case letters.

binom_data() creates a simulated univariate binomial proportion data set having a variable pn representing the number of successes, a variable qn representing the number of failures, and an independent variable iv with levels represented by lower case letters.

Usage

bernoulli_data(
  levels = 5,
  length = 66,
  probs = seq(0.5, 0.1, length.out = levels)
)

binom_data(
  levels = 5,
  length = 66L,
  probs = seq(0.5, 0.1, length.out = levels)
)

Arguments

levels: numeric, the desired number of levels of the independent variable iv; default 5.
length: numeric, the desired number of simulated observations per level of the independent variable iv; default 20.
probs: a numeric vector of the same length as levels, representing the probabilities of success for each corresponding level; default seq(0.5, 0.1, length.out = levels).

Value

An object of class "announce" inheriting from tibble with column iv for the independant variable, and for bernoulli_data(), column dv representing the dependant variable; and for binom_data(), columns pn and qn representing the number of "successes" and "failures", as follows: -

iv: a factor representing levels of the independant variable.
dv: an integer representing the value of the dependent variable.
pn: an integer representing the number of successes.
qn: an integer representing the number of failures.

Details

A random sample from a Bernoulli distribution is obtained for each level of the independent variable iv, at the corresponding probability given in probs, using rbinom() with size = 1. The result is returned as a tibble with two columns, iv representing the level of the independent variable and dv representing the simulated data. The result may be easily converted into (simulated) proportion data and inspected using binom_contingency(), see examples.

A random sample from a binomial distribution of size length is obtained for each level of the independent variable iv, at the corresponding probability given in probs, using rbinom() with size = levels.

bernoulli_data() and binom_data() are used for demonstrating and testing functions such as contingency_table(), binom_contingency() and odds_ratio().

Note

The default length of 66 is the minimum number of trials with probability of success of 0.1 for which the overall probability of zero failures is less than 1 in 1000 i.e., \((1 - 0.1)^{66} < 0.001\).

Examples

bernoulli_data()
#> ___________________________
#> Simulated Bernoulli Data: -
#> 
#> # A tibble: 330 × 2
#>    iv       dv
#>  * <fct> <int>
#>  1 a         1
#>  2 a         0
#>  3 a         0
#>  4 a         1
#>  5 a         1
#>  6 a         0
#>  7 a         1
#>  8 a         0
#>  9 a         1
#> 10 a         0
#> # ℹ 320 more rows
bernoulli_data() |> binom_contingency(dv, iv)
#> _____________________________
#> Binomial Contingency Table: -
#> 
#> # A tibble: 5 × 3
#>   iv       pn    qn
#> * <fct> <int> <int>
#> 1 a        30    36
#> 2 b        26    40
#> 3 c        19    47
#> 4 d        12    54
#> 5 e         5    61
bernoulli_data(probs = seq(0.4, 0, length.out = 5)) |> binom_contingency(dv, iv)
#> _____________________________
#> Binomial Contingency Table: -
#> 
#> # A tibble: 5 × 3
#>   iv       pn    qn
#> * <fct> <int> <int>
#> 1 a        32    34
#> 2 b        17    49
#> 3 c        11    55
#> 4 d         4    62
#> 5 e         0    66

binom_data()
#> __________________________
#> Simulated Binomial Data: -
#> 
#> # A tibble: 5 × 3
#>   iv       pn    qn
#> * <fct> <int> <int>
#> 1 a        31    35
#> 2 b        26    40
#> 3 c        19    47
#> 4 d        14    52
#> 5 e         8    58
binom_data(probs = seq(0.4, 0, length.out = 5))
#> __________________________
#> Simulated Binomial Data: -
#> 
#> # A tibble: 5 × 3
#>   iv       pn    qn
#> * <fct> <int> <int>
#> 1 a        31    35
#> 2 b        17    49
#> 3 c        11    55
#> 4 d         9    57
#> 5 e         0    66